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4. The solution is x = -1, y = -2

5. Both equations represent the same line and the system of equation has Infinitely many solutions

6. The system of equation represent two parallel lines, therefore, the system of equation has no solutions

Step-by-step explanation:

4. The given system of equation are;

y = -3·x - 5...(1)

y = 9·x + 7...(2)

Equating both values of y from the two equations, gives;

9·x + 7 = -3·x - 5

12·x = -5 - 7 = -12

x = -12/12 = -1

x = -1

y = 9·x + 7 = 9 × (-1) + 7 = -2

y  = -2

5. y = -2·x - 5...(1)

6·x + 3·y = -15...(2)

Substituting the value of 'y' from equation (1) in equation (2), gives;

6·x + 3·y = 6·x + 3 × (-2·x - 5) = -15 = -15

Therefore, equations (1) and (2) are the same and has infinitely many solutions

6. y = -4·x + 3

8·x + 2·y = 8

Substituting the value of 'y' from equation (1) in equation (2), gives;

8·x + 2·y = 8·x + 2×(-4·x + 3) = 6

However, 8·x + 2·y = 8, therefore, equations (1) and (2) do not intersect and they have no common solution.

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step-by-step explanation:

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